QUESTION 1 (7 points): Let four existing facilities be located at P = (0, 10), P...

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QUESTION 1 (7 points): Let four existing facilities be located at P₁ = (0, 10), P₂ = (5, 10), P₁ = (5,15) and P₂ = (10,5) with w₁ = 15, W₂ = 20, W3 = 5 and w4 = 30. Assume that the cost is proportional to the Euclidean distance and the objective is to minimize the sum of weighted distances. Existing Facility P1 P₂ P3 P₁ x- Coordinate 0 5 5 10 y-Coordinate 10 10 15 5 Weight 15 20 5 30 a) (3 points) Examine facility P₁ to determine if it is the optimal location for establishing a new single facility. b) (3 points) Examine facility P₂ to determine if it is the optimal location for establishing a new single facility. c) (1 point) What would you do if none of the existing facilities offers the optimal solution, and which algorithm would you choose to apply? d) Exercise (0 point): Create upper and lower bounds for the optimal Euclidean objective function value using the formula below: Bounds: X": Optimal Euclidean solution ₁/2: Optimal values of the rectilinear subproblems X = Any point (e.g. rectilinear solution, centroid solution) (0)² + (²) ≤ f(x) ≤ f(x) QUESTION 1 (7 points): Let four existing facilities be located at P₁ = (0, 10), P₂ = (5, 10), P₁ = (5,15) and P₂ = (10,5) with w₁ = 15, W₂ = 20, W3 = 5 and w4 = 30. Assume that the cost is proportional to the Euclidean distance and the objective is to minimize the sum of weighted distances. Existing Facility P1 P₂ P3 P₁ x- Coordinate 0 5 5 10 y-Coordinate 10 10 15 5 Weight 15 20 5 30 a) (3 points) Examine facility P₁ to determine if it is the optimal location for establishing a new single facility. b) (3 points) Examine facility P₂ to determine if it is the optimal location for establishing a new single facility. c) (1 point) What would you do if none of the existing facilities offers the optimal solution, and which algorithm would you choose to apply? d) Exercise (0 point): Create upper and lower bounds for the optimal Euclidean objective function value using the formula below: Bounds: X": Optimal Euclidean solution ₁/2: Optimal values of the rectilinear subproblems X = Any point (e.g. rectilinear solution, centroid solution) (0)² + (²) ≤ f(x) ≤ f(x)

Answer rating: 100% (QA)

a To determine if P1 is the optimal location calculate the weighted distances from P1 to all other f... View the full answer